1. Field of the Invention
The present invention generally relates to a system for calculating and analyzing critical stresses in a complex completion tube string.
2. Background of the Related Art
In order to access fluids, e.g., hydrocarbons and/or water from subsurface reservoirs, deep well drilling techniques are typically employed. The drilling and completion portion of these techniques generally includes drilling a borehole in the earth and then lining the borehole with a tubular or xe2x80x9ccasingxe2x80x9d to create a wellbore. The borehole is lined in order to support the walls of the borehole and to facilitate the isolation of certain parts of the wellbore to effectively gather fluids from hydrocarbon-bearing formations therearound. Thereafter, an annular area formed between the casing and the borehole may be filled and sealed with cement. The casing may then be perforated at a predetermined location to permit the inflow of fluid from the formation into the wellbore. Because the casing forming the wellbore is not removable if damaged and because drilling and production fluids are often corrosive, a separate, smaller diameter string of tubulars or production tubing is typically inserted coaxially into the wellbore to provide a conduit to the surface for production fluid. The tubing string may include and/or have attached thereto, some length of wellscreen at a lower end whereby production fluid may enter the string while particulate matter carried by the fluid, like formation sand, is filtered out.
To urge the fluids into the production string, an annulus may be formed between the production string and the casing may be sealed with packers above and below the perforated area of the casing. Various types of packers are in use today and their basic functions and operation are well known to those skilled in the art. In general, a packer fits in an annular area between two tubulars and prevents fluids from passing thereby. In the case of a production string within a wellbore, the packer seals the annulus formed between the production string and the casing, thereby preventing the production fluid from traveling to the surface of the well in the annulus. Packers are typically carried into a wellbore on production tubing or some separate run-in string and then remotely actuated with some type of expandable element extending radially outward to contact and seal the casing. In each case, the packer relies on a sealing assembly between the inside diameter of the packer and the outside diameter of the production tubing.
A traditional wellbore may include a string of production tubing several thousand feet in length. The length of the string sections results in enormous weight, at least some of which must be supported in order to prevent the string from buckling and becoming damaged in the wellbore. While the diameter of the tubing is relatively small, the great length of these stings of pipe exaggerates any pressure and/or thermal conditions that are preset in the wellbore. For example, temperatures at the bottom of a wellbore are typically higher than temperatures at the surface of the well. Therefore, the overall length of a production string can increase significantly as a result of these pressure differences. Due to thermal expansion, conversely, in some well treatment programs, relatively cool fluids are pumped in and around a production string of tubulars and the overall length of the string can actually decrease in these instances. Similarly, differences in pressures may also cause a tube string to either expand or contract, depending upon the situation.
A change in the length of production strings is especially critical to the operation of packers. Because packers rely upon an interaction of sealing members on the tubing and the packer, any axial movement of the tubing with respect to the packer can cause the sealing members to lose contact with one another and the packer to become ineffective. In some cases, tubing is supplied with extended sealing surfaces to compensate for expected tubing string movement due to thermal expansion and contraction. However, these remedies are not always effective if the conditions of the well are such that a change in tubing length is unforeseen or is greater than expected. Therefore, prior to implementing a completion system, often the physical characteristics of the tube string are analyzed in order to accurately determine the forces that may be acting on the tube string during operation. This analysis may then be used to modify the design of the tube string in order to reduce the possibility of breaking and/or buckling as a result of excessive stresses on the tube string.
The basic application of mathematical principles for calculation and analysis of forces in single string completion systems was presented by Lubinski, Althouse, and Logan in a paper entitled xe2x80x9cHelical Buckling of Tubing Sealed in Packersxe2x80x9d in October of 1961. Although Lubinski clearly addressed the basic linear mathematical equations and procedures necessary to analyze the single string completions of the 1960""s, the drilling industry quickly progressed past simple single string completions into more complex combination-type completion systems. Stress analysis work was also postulated by Durham in a paper entitled xe2x80x9cTubing Movement, Forces, and Stresses in Dual Flow Assembly Installationsxe2x80x9d in 1980. Therefore, in an attempt to analyze these combination-type completion systems, Hammerlindl published an article entitled xe2x80x9cMovement, Forces, and Stresses Associated with Combination Tubing Strings Sealed in Packersxe2x80x9d in 1977, which was essentially an analytical xe2x80x9cextensionxe2x80x9d of the linear single string principles espoused by Lubinski. As a result of Hammerlindl""s xe2x80x9cextensionxe2x80x9d approach to combination-type completion systems, the tenets of Lubinski were applied to combination systems, which resulted in inaccurate analysis of complex completion systems.
As an example of a possible inaccuracy in Hammerlindl""s extension-type principles, consider application of a linear single-string completion analysis to a complex completion system, such as the exemplary system shown in FIG. 2, for the purpose of determining the change in length of the tube string due to a ballooning effect through linear superposition techniques. In calculating the change in length using Hammerlindl""s method, the change in length for each section is calculated and the sum of the individual calculations are added together to generate a solution for the entire complex tube string. The equation for calculating the change in length is shown below as equation (1).                               Δ          ⁢                      xe2x80x83                    ⁢                      L            3                          =                                                            V                ⁢                                  xe2x80x83                                ⁢                                  L                  2                                            E                        ⁢                                                            Δ                  ⁢                                      xe2x80x83                                    ⁢                                      ρ                    t                                                  -                                                      R                    2                                    ⁢                  Δ                  ⁢                                      xe2x80x83                                    ⁢                                      ρ                    c                                                  -                                                                            1                      +                                              2                        ⁢                        v                                                                                    2                      ⁢                      v                                                        ⁢                  δ                                                                              R                  2                                -                1                                              -                                                    2                ⁢                v                ⁢                                  xe2x80x83                                ⁢                L                            E                        ⁢                                                            Δ                  ⁢                                      xe2x80x83                                    ⁢                                      P                    t                                                  -                                                      R                    2                                    ⁢                  Δ                  ⁢                                      xe2x80x83                                    ⁢                                      P                    c                                                                                                R                  2                                -                1                                                                        (        1        )            
However, upon careful consideration of the application of the superposition principle to equation (1), Applicants submit that the result obtained by Hammerlindl may not be 100% accurate in all situations. For example, Applicants submit that the calculation method of Hammerlindl does not consider the state of the tube string in the calculation, and therefore, if the state of the tube string is not as Hammerlindl assumes, an inaccurate result may be obtained.
Similar examples may be found in Hammerlindl""s application of Lubinski""s analytical theory to complex completion systems with regard to the calculation of buoyancy effects, the calculation of buckling effects, and the calculation of the slack off forces reaching a packer in a situation where the tube string is in contact with the casing at one or more locations in the well bore. Therefore, in view of these deficiencies, there exists a clear need for a completion systems tube string analysis system and/or method capable of accurately analyzing modem complex completion systems.
The present invention provides a method for analysing a well completion system, wherein the method includes receiving data representative of physical characteristics of the completion system and calculating a first change in length of a tube string resulting from a helical buckling effect. The method further includes calculating a second change in length of the tube string resulting from a ballooning effect and calculating a third change in length of the tube string resulting from a slackoff force effect. Upon completion of the calculating steps, the method may output predetermined results therefrom.
The present invention further provides a method for analysing a well completion system, wherein the method includes receiving input data representative of physical and environmental characteristics of the completion system and determining a change in length for each individual tube section of a tube string. The method further includes determining a total change in length of the tube string through summing the change in length determined for each individual tube section of the tube string, and outputting results of the determining step to the user.
The present invention further provides a signal-bearing medium having a completion system analysis program thereon. When one or more processors execute the program, a method for analysing a completion system is undertaken. The analysis method includes receiving data representative of physical characteristics of the completion system, and calculating a first change in length of a tube string resulting from a helical buckling effect. The method further includes calculating a second change in length of the tube string resulting from a ballooning effect and calculating a third change in length of the tube string resulting from a slackoff force effect. The results of the calculating steps, or at least predetermined portions thereof, may be outputted and/or displayed to a user.
The present invention further provides a signal-bearing medium containing a program for analysing a completion system that when executed by a processor performs a method for analysing characteristics of a completion system. The method may include the steps of receiving input data representative of physical and environmental characteristics of the completion system, determining a change in length for each individual tube section of a tube string, and determining a total change in length of the tube string through summing the change in length determined for each individual tube section of the tube string. Once these steps are conducted, the method may include the step of outputting results of the determining steps to the user.